1mathieu0.mac and mathieu.mac are from the book "Computer Algebra in 2Applied Mathematics: An introduction to MACSYMA", by Richard H Rand, 3Pitman (1984). 4 5Mathieu's equation is x''+(delta+e*cos(t))*x=0 6 7For given values of the parameters delta and e, either all the 8solutions are bounded (the equation is stable) or there exist 9unbounded solutions (the equation is unstable). The regions of 10stability are separated from thos of instability by "transition 11curves". 12 13This program computes the transition curves for n=0 (mathieu0.mac) and 14n>0 (mathieu.mac) in Mathieu's equation using a perturbation method. 15 16The run below, using maxima-5.9.0cvs, reproduces the result on pages 1790-94 of the book. 18 19(C1) load("./mathieu0.mac"); 20(D1) ./mathieu0.mac 21(C2) mathieu0(); 22ENTER DEGREE OF TRUNCATION 238; 24 8 6 4 2 25 68687 e 29 e 7 e e 26delta= -------- - ----- + ---- - -- 27 294912 144 32 2 28 29 30(C1) load("./mathieu.mac"); 31(D1) ./mathieu.mac 32(C2) mathieu(); 33ENTER TRANSITION CURVE NUMBER N 341; 35ENTER DEGREE OF TRUNCATION 366; 37 6 5 4 3 2 38 49 e 11 e e e e e 1 39delta= ----- - ----- - --- + -- - -- - - + - 40 36864 4608 384 32 8 2 4 41 42 6 5 4 3 2 43 49 e 11 e e e e e 1 44delta= ----- + ----- - --- - -- - -- + - + - 45 36864 4608 384 32 8 2 4 46 47(D2) 48(C3) mathieu(); 49ENTER TRANSITION CURVE NUMBER N 502; 51ENTER DEGREE OF TRUNCATION 526; 53 6 4 2 54 1002401 e 763 e 5 e 55delta= ---------- - ------ + ---- + 1 56 4976640 3456 12 57 58 6 4 2 59 289 e 5 e e 60delta= - ------- + ---- - -- + 1 61 4976640 3456 12 62 63 64Local Variables: *** 65mode: Text *** 66End: ***